Solution
= Solution
The <cosmological constant energy> is constant, whereas the <matter density> scales as $a^{-3}$. Hence
$$
\rho_{\rm dust}(a)=\rho_{\rm cc}
\left(\frac{a_{\rm eq}}a\right)^3.
$$
The transition occurs when $\rho+3P=\rho_{\rm dust}-2\rho_{\rm cc}=0$, so
$$
\left(\frac{a_{\rm eq}}a\right)^3=2,
\qquad
\boxed{\frac a{a_{\rm eq}}=2^{-1/3}.}
$$